I juice mainly green vegetables: kale, spinach, etc, then carrots -and it doesn't have enough power, slows down and then stops - any idea why?

There's nothing wrong. These juicers do not eject the pulp and go out of balance very
easily. If you continue to have problems you may have to go for a different type of juicer.
The Hurom or Omega VRT, expensive, look good if you're really into juicing.

If you mean green leafy greens, the juicer is
not really designed for them. A sharp blade
will extract some juice from them, but I found
a new blade seems to increase the vibration
issue. Acme works best on carrots, apples,
celery, etc.

The higher the pressure the harder the machine squeezes and the dryer the pulp. Leafy Greens and wheatgrass can use Setting "3". Carrots, beets and hard items are best on setting "2"

nope

I have a brand new one from Costco and it goes through carrots very quickly.

FIRST DUMP THE FILTERS, THEY DECREASE YIELD AND MAY CAUSE MORE VIBRATION.
IF JUICER SHUTS DOWN PUSH RESET BUTTON ON BOTTOM. THIS TYPE OF JUICER DOES
NOT EJECT PULP AND REQUIRES SOME TIME TO MASTER. FEED THE STUFF SLOW AND
STEADY. WANT A GOOD JUICE? TRY 1 APPLE, 2 CARROTS, 2 CELERY AND A HALF LEMON.
IF YOU ARE REALLY BRAVE YOU CAN FINISH OFF BY SLOWLY POURING 6 OR 8 OUNCERS
OF WATER RIGHT DOWN THE CHUTE. THIS NOT ONLY DILUTES BUT LEECHES MORE JUICE
OUT OF THE PULP. JUICE SHOULD BE DILUTED AND DRANK SLOWLY.

use a quatered apple in between carrort.

you are pushing too hard, this machine likes it slow.

Parts from Champion website. You may need a new cutter, sometimes cheaper on ebay.

1-800-233-9054, or online at foxinternational.com if you are in the U.S.A. I am pretty certain they will have it. I lost mine--& use a long carrot to push whatever through. If some of the carrot gets juiced--no problem. It is good for you, & tasted great!